namespace Eigen {

namespace internal {

    // TODO : move this to GivensQR once there's such a thing in Eigen

    template <typename Scalar>
    void r1mpyq(DenseIndex m, DenseIndex n, Scalar* a, const std::vector<JacobiRotation<Scalar>>& v_givens, const std::vector<JacobiRotation<Scalar>>& w_givens)
    {
        typedef DenseIndex Index;

        /*     apply the first set of givens rotations to a. */
        for (Index j = n - 2; j >= 0; --j)
            for (Index i = 0; i < m; ++i)
            {
                Scalar temp = v_givens[j].c() * a[i + m * j] - v_givens[j].s() * a[i + m * (n - 1)];
                a[i + m * (n - 1)] = v_givens[j].s() * a[i + m * j] + v_givens[j].c() * a[i + m * (n - 1)];
                a[i + m * j] = temp;
            }
        /*     apply the second set of givens rotations to a. */
        for (Index j = 0; j < n - 1; ++j)
            for (Index i = 0; i < m; ++i)
            {
                Scalar temp = w_givens[j].c() * a[i + m * j] + w_givens[j].s() * a[i + m * (n - 1)];
                a[i + m * (n - 1)] = -w_givens[j].s() * a[i + m * j] + w_givens[j].c() * a[i + m * (n - 1)];
                a[i + m * j] = temp;
            }
    }

}  // end namespace internal

}  // end namespace Eigen
